Department of Mathematicshttp://hdl.handle.net/1957/13737
Sat, 11 Jul 2015 16:24:06 GMT2015-07-11T16:24:06ZThe Variable Speed Wave Equation and Perfectly Matched Layershttp://hdl.handle.net/1957/56308
The Variable Speed Wave Equation and Perfectly Matched Layers
Kim, Dojin
A perfectly matched layer (PML) is widely used to model many different types of wave propagation in different media. It has been found that a PML is often very effective and also easy to set, but still many questions remain.
We introduce a new formulation from regularizing the classical Un-Split PML of the acoustic wave equation and show the well-posedness and numerical efficiency. A PML is designed to absorb incident waves traveling perpendicular to the PML, but there is no effective absorption of waves traveling with large incident angles. We suggest one method to deal with this problem and show well-posedness of the system, and some numerical experiments. For the 1-d wave equation with a constant speed equipped a PML, stability and the exponential decay rate of energy has been proved, but the question for variable sound speed equation remained open. We show that the energy decays exponentially in the 1-d PML wave equation with variable sound speed.
Most PML wave equations appear as a first-order hyperbolic system with as a zero-order perturbation. We introduce a general formulation and show well-posedness and stability of the system. Furthermore we develop a discontinuous Galerkin method and analyze both the semi-discrete and fully discretized system and provide a priori error estimations.
Graduation date: 2016
Thu, 04 Jun 2015 00:00:00 GMThttp://hdl.handle.net/1957/563082015-06-04T00:00:00ZThe Physical Mirror Equivalence for the Local P²http://hdl.handle.net/1957/55868
The Physical Mirror Equivalence for the Local P²
Cacciatori, Sergio Luigi; Compagnoni, Marco; Guerra, Stefano
In this paper we consider the total space of the canonical bundle of P² and we use a proposal by Hosono, together with results of Seidel and Auroux–Katzarkov–Orlov, to deduce the physical mirror equivalence between D[superscript b][subscript P²] (K[subscript P²]) and the derived Fukaya category of its mirror which assigns the expected central charge to BPS states. By construction, our equivalence is compatible with the mirror map relating the complex and the Kähler moduli spaces and with the computation of Gromov–Witten invariants.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/220
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/1957/558682015-01-01T00:00:00ZThe unified discrete surface Ricci flowhttp://hdl.handle.net/1957/55785
The unified discrete surface Ricci flow
Zhang, Min; Guo, Ren; Zeng, Wei; Luo, Feng; Yau, Shing-Tung; Gu, Xianfeng
Ricci flow deforms the Riemannian metric proportionally to the
curvature, such that the curvature evolves according to a heat diffusion process
and eventually becomes constant everywhere. Ricci flow has demonstrated its
great potential by solving various problems in many fields, which can be hardly
handled by alternative methods so far.
This work introduces the unified theoretic framework for discrete Surface
Ricci Flow, including all the common schemes: Tangential Circle Packing,
Thurston’s Circle Packing, Inversive Distance Circle Packing and Discrete
Yamabe Flow. Furthermore, this work also introduces a novel schemes, Virtual
Radius Circle Packing and the Mixed Type schemes, under the unified
framework. This work gives explicit geometric interpretation to the discrete
Ricci energies for all the schemes with all back ground geometries, and the
corresponding Hessian matrices.
The unified frame work deepens our understanding to the the discrete surface
Ricci flow theory, and has inspired us to discover the new schemes, improved
the flexibility and robustness of the algorithms, greatly simplified the
implementation and improved the efficiency.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/graphical-models/
Mon, 01 Sep 2014 00:00:00 GMThttp://hdl.handle.net/1957/557852014-09-01T00:00:00ZOn normalized multiplicative cascades under strong disorderhttp://hdl.handle.net/1957/55716
On normalized multiplicative cascades under strong disorder
Dey, Partha S.; Waymire, Edward C.
See article for Abstract.
This is the publisher’s final pdf. The published article is copyrighted by the author(s) and published by the Institute of Mathematical Statistics. The published article can be found at: http://ecp.ejpecp.org/index.
Wed, 01 Apr 2015 00:00:00 GMThttp://hdl.handle.net/1957/557162015-04-01T00:00:00Z